Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?

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Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?

Richard Hake
Do We Learn All the Math We Need For Ordinary Life Before
Some subscribers to Math-Teach might be interested in a recent post "Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?" [Hake (2013)].  The abstract reads:

*******************************************
ABSTRACT: In response to my post "Einstein on Testing" [Hake (2013)] at <http://bit.ly/UHjqET> the following lively exchange was recorded on the archives <http://yhoo.it/iNTxrH> of EDDRA2 [non-subscribers may have to set up a "Yahoo account" as instructed at <http://yhoo.it/iNTxrH>]:

a. Literature major and Standardista-basher Susan Ohanian <
http://www.susanohanian.org/> stated that she (paraphrasing) "never seemed to gain any insight from solving the calculus problems in Courant's text, which struck her then as plodding and now as without meaning."

b. Susan Harman then opined (my CAPS) "WE LEARN ALL THE MATH WE NEED FOR ORDINARY LIFE BEFORE 5TH GRADE."

c. Guy Brandenberg countered by calling attention to David Berlinski's "Tour of the Calculus" <http://amzn.to/11sZIUv> whose publisher states: "Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall."

d. And Susan Ramlo made the point that students in her algebra-based physics class "almost always make a comment about how suddenly . . .[[after exposure to the *real-world* of physics]]. . .  much more of calculus makes sense."

With regard to Harman's opinion that "We Learn All the Math We Need For Ordinary Life Before 5th Grade," basic to "ordinary life" is motion and change, requiring the rudiments of calculus for proper understanding (see the Bartlett signature quote).

And I agree with Ramlo's point about students' better understanding calculus after exposure to the *real world* of physics. In "Interactive-engagement methods in introductory mechanics courses" at <http://bit.ly/aH2JQN> I wrote: "the term 'substantive non-calculus-based mechanics course' is an oxymoron."
***************************************************

To access the complete 13 kB post please click on <http://bit.ly/10sYmKl>.

Richard Hake, Emeritus Professor of Physics, Indiana University
Links to Articles: <http://bit.ly/a6M5y0>
Links to Socratic Dialogue Inducing (SDI) Labs: <http://bit.ly/9nGd3M>
Academia: <http://bit.ly/a8ixxm>
Blog: <http://bit.ly/9yGsXh>
GooglePlus: <http://bit.ly/KwZ6mE>

"The greatest shortcoming of the human race is our inability to understand exponential change."
     - Albert Bartlett <http://bit.ly/VpN2pm> [I have taken the liberty of substituting
       "exponential change" for Bartlett's more esoteric "the exponential function."]

REFERENCES [URL shortened by <http://bit.ly/> and accessed on 13 Jan 2013.] 
Hake, R.R. 2013."Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?" online on the OPEN! AERA-L archives at <http://bit.ly/10sYmKl>. Post of 13 Jan 2013 16:52:01-0800 to AERA-L and Net-Gold. The abstract and link to the complete post are being transmitted to several discussion lists and are also on my blog "Hake'sEdStuff" at <http://bit.ly/RQkucu> with a provision for comments.
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Re: Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?

GS Chandy
Richard Hake posted Jan 14, 2013 10:33 PM:
>
> Some subscribers to Math-Teach might be interested in
> a recent post
> "Do We Learn All the Math We Need For Ordinary Life
> Before 5th
> Grade?" [Hake (2013)].  The abstract reads:
<snip>

>
> a. Literature major and Standardista-basher Susan
> Ohanian
> <http://www.susanohanian.org/> stated that she
> (paraphrasing) "never
> seemed to gain any insight from solving the calculus
> problems in
> Courant's text, which struck her then as plodding and
> now as without meaning."
>
> b. Susan Harman then opined (my CAPS) "WE LEARN ALL
> THE MATH WE NEED FOR ORDINARY LIFE BEFORE 5TH GRADE."
>
<snip>
>
Well, sure.  I agree with these ladies.

In fact, we all do happen to learn all the language and literature, all the history and geography, economics and (gulp) philosophy, math, chemistry abd physics that we need for 'ORDINARY LIFE' before we finish 6th grade (perhaps even the 5th grade).

But some (or a great many) of us seem to want a bit more than that 'ordinary life' Ms Harman seems to yearn for.

I'm pretty certain that Ms Harman would have been able to write all of her very ordinary thoughts in her very ordinary article with the ordinary knowledge she had gained of all of these subjects before she left her 5th grade.  Society should therefore give her and people like her exactly what they want - a 5th grade education.

Further, it is in fact entirely clear that Ms Susan Ohanian gained no insights whatsoever from doing a calculus problem in Courant.  

Her thoughts do strike me as plodding, but meaningful.  

The meaning is that some of us should quit school at 5th grade or sooner.

GSC
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Re: Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?

Dave L. Renfro
In reply to this post by Richard Hake
Richard Hake wrote (in part):

http://mathforum.org/kb/message.jspa?messageID=8067464

> ABSTRACT: In response to my post "Einstein on Testing" [Hake (2013)]
> at <http://bit.ly/UHjqET> the following lively exchange was recorded
> on the archives <http://yhoo.it/iNTxrH> of EDDRA2 [non-subscribers
> may have to set up a "Yahoo account" as instructed at
> <http://yhoo.it/iNTxrH>]:
>
> a. Literature major and Standardista-basher Susan Ohanian
> <http://www.susanohanian.org/> stated that she (paraphrasing) "never
> seemed to gain any insight from solving the calculus problems in
> Courant's text, which struck her then as plodding and now as without
> meaning."

Courant's book is definitely a classic, regardless of whether she's
talking about the 1937 translation by McShane or the very similar
version co-authored with Fritz John that came out in 1966. I base
this on the many reviews I have at home of the various versions of
Courant's book (in my extensive collection of math book reviews)
and on the 1966 version that I've owned since about 1973 (and
which I have often mentioned in various internet posts over the
years, a few of which are listed below for those interested [1]).

Being a bit amazed that a literature major would be working through
Courant's book, I looked up the post that Richard Hake took this
from. What follows is a bit more detail about the Courant book matter:

http://groups.yahoo.com/group/EDDRA2/message/3602

* I like to tell the story that Hans, a newly minted Ph.D. in physics was
* stunned to find out he was married to somebody who never took calculus.
* I don't know quite what he expected from an MA in medieval literature,
* but the first year we were married he gave me an ugly calculus book for
* Xmas, explaining it was a classic in the field (Courant). The second
* year we were married I gave him a notebook with the problems worked out.
* I never seemed to gain any insight from this exercise, which struck me
* then as plodding and now I don't have any idea what any of it means.
* Nonetheless, doing calculus for love is a far better reason than the
* one promoted by Obama, Duncan, Bill Gates, et al.

Wow, this sure sounds fishy to me! First, and this part isn't fishy,
the fact that Hans thought to recommend Courant's book to her (given
her situation) strikes me as really naive and out-of-touch. I'd like to
say I'm stunned to find that a Ph.D. in physics would think Courant's
book was appropriate for her, but unfortunately I'm not. Second, and
this is the fishy part, I simply don't believe she (correctly) worked
even 20% of the problems, and yet her wording "with the problems worked
out" suggests she worked all of them (or at least, her wording was carefully
constructed to leave this possibility open). Indeed, quite a few of the
problems--perhaps as many as a third of them--are challenging enough that I
would expect the average (U.S.) upper level undergraduate math major
to have difficulty with them. Also, the words "plodding" and "no insight"
don't fit with the problems in Courant's book. It's as if someone said
she had carefully read all 3 volumes of "The Feynman Lectures On Physics"
and found the endeavor to be plodding and gave no insight into physics.

[1] http://tinyurl.com/b9stek4
http://mathforum.org/kb/message.jspa?messageID=4071934
http://mathforum.org/kb/message.jspa?messageID=4126649
http://mathforum.org/kb/message.jspa?messageID=4161088
http://mathforum.org/kb/message.jspa?messageID=6122912
http://math.stackexchange.com/questions/79865/difficulty-level-of-courants-book

Dave L. Renfro

P.S. For what it's worth, I've also never taken a calculus course.
This, of course, shows that we shouldn't equate having taken a course
in Subject X with knowing Subject X. Neither implies the other, and I
can find counterexamples for both directions in my own experience.
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Re: Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?

GS Chandy
In reply to this post by Richard Hake
Responding to Dave Renfro's post dt. Jan 15, 2013 2:57 AM (which is pasted below my signature for ready reference):

Thanks for that excellent (and most enlightening) response, Dave!  I very much endorse your P.S. to the effect that 'having taken a course on subject X' does not imply 'having UNDERSTOOD subject X' (or vice versa).

I believe the links in your message you've provided to previous relevant correspondence are of great value.  

I did go through a fair bit of that correspondence - some of it quite assiduously, indeed with paper and pencil in hand! (I must confess I did falter at several points, particularly when for adequate understanding I should have dug out old Calculus texts and the like - I simply do not have that kind of access readily available now).  

I'm happy to observe that (at one particular thread discussing some quite subtle points on 'limits') one R. Colacitti was duly grateful to you and others who helped him with his doubts on "derivative using first principles NOT EQUAL TO derivative using power rule".  (I wish I'd had something like such an Internet backup resource available when I was studying Calculus myself, way back when - I'm sure I would have gained a far deeper understanding than I did manage to do).

In particular, wrt the posts at "The Unapologetic Mathematician" - which I confess I did NOT work through in detail as it is huge - I was interested to observe that 'our usual suspect' Haim is present in quite his 'usual form'.  Lou Talman came up there with a classic (NOT in response to Haim):

"Mathematics involves ideas as well as skills. Teaching either while ignoring the other is unconscionable".  

(My observation here is that we too often find examples of the ideas AND the skills both not being explored adequately. This is often the case alas even in basic logical thought processes even aside from any mathematics).

Thanks for having explored that post from which Richard Hake had taken his tale.  You're entirely correct in your observation that it smells more than a bit fishy that a "literature major would be working through Courant's book" and her (implied) claim of having worked through 'all of the problems' is even fishier - in fact, it stinks right to high heaven.  

As I recall, several of those problems were pretty challenging for me - and I used to possess some fair skills in math, particularly in calculus!

All said and done, I feel I probably could repeat my earlier observation that some may as well quit schooling by 5th grade or even earlier for all the good that schooling has done for them.  This is not to imply that we should cease efforts to educate our youth (as well as others):  what really needs to be done is, as I've claimed before, "to redesign our educational [and many other] systems".

GSC

Dave L. Renfro posted Jan 15, 2013 2:57 AM:

> Richard Hake wrote (in part):
>
> http://mathforum.org/kb/message.jspa?messageID=8067464
>
> > ABSTRACT: In response to my post "Einstein on
> Testing" [Hake (2013)]
> > at <http://bit.ly/UHjqET> the following lively
> exchange was recorded
> > on the archives <http://yhoo.it/iNTxrH> of EDDRA2
> [non-subscribers
> > may have to set up a "Yahoo account" as instructed
> at
> > <http://yhoo.it/iNTxrH>]:
> >
> > a. Literature major and Standardista-basher Susan
> Ohanian
> > <http://www.susanohanian.org/> stated that she
> (paraphrasing) "never
> > seemed to gain any insight from solving the
> calculus problems in
> > Courant's text, which struck her then as plodding
> and now as without
> > meaning."
>
> Courant's book is definitely a classic, regardless of
> whether she's
> talking about the 1937 translation by McShane or the
> very similar
> version co-authored with Fritz John that came out in
> 1966. I base
> this on the many reviews I have at home of the
> various versions of
> Courant's book (in my extensive collection of math
> book reviews)
> and on the 1966 version that I've owned since about
> 1973 (and
> which I have often mentioned in various internet
> posts over the
> years, a few of which are listed below for those
> interested [1]).
>
> Being a bit amazed that a literature major would be
> working through
> Courant's book, I looked up the post that Richard
> Hake took this
> from. What follows is a bit more detail about the
> Courant book matter:
>
> http://groups.yahoo.com/group/EDDRA2/message/3602
>
> * I like to tell the story that Hans, a newly minted
> Ph.D. in physics was
> * stunned to find out he was married to somebody who
> never took calculus.
> * I don't know quite what he expected from an MA in
> medieval literature,
> * but the first year we were married he gave me an
> ugly calculus book for
> * Xmas, explaining it was a classic in the field
> (Courant). The second
> * year we were married I gave him a notebook with the
> problems worked out.
> * I never seemed to gain any insight from this
> exercise, which struck me
> * then as plodding and now I don't have any idea what
> any of it means.
> * Nonetheless, doing calculus for love is a far
> better reason than the
> * one promoted by Obama, Duncan, Bill Gates, et al.
>
> Wow, this sure sounds fishy to me! First, and this
> part isn't fishy,
> the fact that Hans thought to recommend Courant's
> book to her (given
> her situation) strikes me as really naive and
> out-of-touch. I'd like to
> say I'm stunned to find that a Ph.D. in physics would
> think Courant's
> book was appropriate for her, but unfortunately I'm
> not. Second, and
> this is the fishy part, I simply don't believe she
> (correctly) worked
> even 20% of the problems, and yet her wording "with
> the problems worked
> out" suggests she worked all of them (or at least,
> her wording was carefully
> constructed to leave this possibility open). Indeed,
> quite a few of the
> problems--perhaps as many as a third of them--are
> challenging enough that I
> would expect the average (U.S.) upper level
> undergraduate math major
> to have difficulty with them. Also, the words
> "plodding" and "no insight"
> don't fit with the problems in Courant's book. It's
> as if someone said
> she had carefully read all 3 volumes of "The Feynman
> Lectures On Physics"
> and found the endeavor to be plodding and gave no
> insight into physics.
>
> [1] http://tinyurl.com/b9stek4
> http://mathforum.org/kb/message.jspa?messageID=4071934
> http://mathforum.org/kb/message.jspa?messageID=4126649
> http://mathforum.org/kb/message.jspa?messageID=4161088
> http://mathforum.org/kb/message.jspa?messageID=6122912
> http://math.stackexchange.com/questions/79865/difficul
> ty-level-of-courants-book
>
> Dave L. Renfro
>
> P.S. For what it's worth, I've also never taken a
> calculus course.
> This, of course, shows that we shouldn't equate
> having taken a course
> in Subject X with knowing Subject X. Neither implies
> the other, and I
> can find counterexamples for both directions in my
> own experience.
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Re: Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?

Dave L. Renfro
In reply to this post by Richard Hake
Dave L. Renfro wrote (in part):

http://mathforum.org/kb/message.jspa?messageID=8067932

> the fact that Hans thought to recommend Courant's book to her (given
> her situation) strikes me as really naive and out-of-touch. I'd like to
> say I'm stunned to find that a Ph.D. in physics would think Courant's
> book was appropriate for her, but unfortunately I'm not.

It occurs to me that it's easy to make a hit-and-run criticism like
this, and a bit difficult to offer an appropriate alternative. To this
end, I think the following books would have worked better for her:

Silvanus Phillips Thompson, "Calculus Made Easy", 2nd edition, 1914.
http://www.gutenberg.org/files/33283/33283-pdf.pdf

David Berlinski, "A Tour of the Calculus", 1997.
http://www.amazon.com/dp/0679747885

Dave L. Renfro
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Re: Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?

Robert Hansen
Other than your's (and mine) puzzlement over the author's statement regarding "working out the problems", isn't this just the expected and unavoidable consequence of people studying what they weren't meant to study, and then telling us of it?

Bob Hansen


On Jan 15, 2013, at 10:23 AM, Dave L. Renfro <[hidden email]> wrote:

> Dave L. Renfro wrote (in part):
>
> http://mathforum.org/kb/message.jspa?messageID=8067932
>
>> the fact that Hans thought to recommend Courant's book to her (given
>> her situation) strikes me as really naive and out-of-touch. I'd like to
>> say I'm stunned to find that a Ph.D. in physics would think Courant's
>> book was appropriate for her, but unfortunately I'm not.
>
> It occurs to me that it's easy to make a hit-and-run criticism like
> this, and a bit difficult to offer an appropriate alternative. To this
> end, I think the following books would have worked better for her:
>
> Silvanus Phillips Thompson, "Calculus Made Easy", 2nd edition, 1914.
> http://www.gutenberg.org/files/33283/33283-pdf.pdf
>
> David Berlinski, "A Tour of the Calculus", 1997.
> http://www.amazon.com/dp/0679747885
>
> Dave L. Renfro

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Re: Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?

Dave L. Renfro
In reply to this post by Richard Hake
Robert Hansen wrote:

http://mathforum.org/kb/message.jspa?messageID=8070385

> Other than your's (and mine) puzzlement over the author's statement regarding
> "working out the problems", isn't this just the expected and unavoidable
> consequence of people studying what they weren't meant to study, and then
> telling us of it?

Perhaps, but working through Courant's calculus text under those
circumstances borders on superhuman drive. She did say that it
was a Christmas present and that she worked through it "for love"
(of her husband), but I suspect even the average physics Ph.D.
(she said her husband is a physics Ph.D.), prior to learning calculus,
wouldn't have the drive to work through Courant's Calculus
on his/her own, even for love.

While I'm at it, here's another more suitable Christmas present
to go with the two books I've already suggested:

W. W. Sawyer, "What is Calculus About?", 1962.
http://www.amazon.com/dp/0883856026

Dave L. Renfro
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Re: Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?

Richard Hake
In reply to this post by Richard Hake
Re: Do We Learn All the Math We Need For Ordinary Life Bef
With no apologies for cross posting - see e.g. "Cross-Posting - Synergistic or Sinful?" [Hake (2005)].

If you reply to this long (9 kB) post please don't hit the reply button unless you prune the copy of this post that may appear in your reply down to a few relevant lines, otherwise the entire already archived post may be needlessly resent to subscribers.

In response to my post "Do We Learn All the Math We Need For Ordinary Life Before 5th_Grade?" [Hake (2013)], math guru <http://bit.ly/Xbd0ye> Dave Renfro (2013a) in his Math-Teach post wrote [bracketed by lines "RRRR. . . "; slightly edited;  my insert at ". . . .[[insert]]. . . . "]:

RRRRRRRRRRRRRRRRRRRRRRRRRRRRR
In my previous post "Do We Learn All the Math We Need For Ordinary Life Before 5th_Grade?" [Renfro (2013b)] I wrote:

". . . the fact that Hans Ohanian, author of "Einstein's Mistakes" [Ohanian (2009)], thought to recommend Courant's book to his wife, literature major Susan Ohanian <http://www.susanohanian.org>, strikes me as really naive and out-of-touch. I'd like to say I'm stunned to find that a Ph.D. in physics would think Courant's book was appropriate for her, but unfortunately I'm not."

It occurs to me that it's easy to make a hit-and-run criticism like this, and a bit difficult to offer an appropriate alternative. To this end, I think the following books would have worked better for her:

1. Silvanus Phillips Thompson, "Calculus Made Easy", 2nd edition, 1914. FREE at
<http://www.gutenberg.org/files/33283/33283-pdf.pdf>.

2. David Berlinski, "A Tour of the Calculus", 1997. <http://www.amazon.com/dp/0679747885>
RRRRRRRRRRRRRRRRRRRRRRRRRRRRR

I reference "A Tour of the Calculus" [Berlinski (1997)] in my post "Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?"

In my opinion, some other calculus texts (had they been available at the time) that might have worked better than Courant's book [e.g. Courant & John (1998)] for Susan Ohanian are:

3. "Calculus: An Intuitive and Physical Approach" Kline (1998).
4. "Basic Calculus: From Archimedes to Newton to it's Role in Science" [Hahn (1998).

5. "Applied Calculus" [Hughes-Hallett et al. (2009)].

Richard Hake, Emeritus Professor of Physics, Indiana University
Links to Articles: <http://bit.ly/a6M5y0>
Links to Socratic Dialogue Inducing (SDI) Labs: <http://bit.ly/9nGd3M>
Academia: <http://bit.ly/a8ixxm>
Blog: <http://bit.ly/9yGsXh>
GooglePlus: <http://bit.ly/KwZ6mE>
Twitter: <http://bit.ly/juvd52>

"Mathematics is the gate and key of the sciences. . . .Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of this world. And what is worse, men who are thus ignorant are unable to perceive their own ignorance and so do not seek a remedy."
        Roger Bacon (Opus Majus, bk. 1, ch. 4) <http://bit.ly/dzjbWv>

REFERENCES [URL shortened by <http://bit.ly/> and accessed on 15 Jan 2013.]
Berlinski, D. 1997. "Tour of the Calculus." Random House, publisher's information at  <http://bit.ly/ZLSHJo>. Amazon.com information at <http://amzn.to/11sZIUv>, note the searchable "Look Inside" feature. An expurgated Google book preview is online at <http://bit.ly/UI4kPC>.

Courant, R. & F. John. 1998. "Introduction to Calculus and Analysis," Vol. 1, Springer, originally published in 1965. Amazon.com information at <http://amzn.to/MqvtkP> note the searchable "Look Inside" feature.

Hahn, A.J. 1998. "Basic Calculus: From Archimedes to Newton to it's Role in Science." Springer. Amazon.com information at <http://amzn.to/LaakMh>. For a review see the late physicist David Halliday (1999).

Hake, R.R. 2005. "Cross-Posting - Synergistic or Sinful?" Post of 1 Nov 2005 08:37:12-0800 to
ITFORUM and AERA-L. Online at on the OPEN! AERA-L archives at <
http://bit.ly/arFlkd>.

Hake, R.R. 2013. "Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?" online on the OPEN! AERA-L archives at <http://bit.ly/10sYmKl>. Post of 13 Jan 2013 16:52:01-0800 to AERA-L and Net-Gold. The abstract and link to the complete post are being transmitted to several discussion lists and are also on my blog "Hake'sEdStuff" at <http://bit.ly/RQkucu> with a provision for comments.

Halliday, D. 1999.  Review of Hahn (1998), Phys. Today 52(4): 74; online to subscribers at 
<http://bit.ly/LbalBm>. Halliday wrote:
"The author, a professor of mathematics at the University of Notre Dame, has used this book in a two-semester calculus sequence 'for arts and letters honors students' and a one-semester course of 'elementary applications of the calculus for regular arts and letters students and architecture majors.' It seems to me that the book is very suitable for such courses. It is perhaps less suitable for a course in which the aim is to learn calculus as a tool and the desire is 'to get on with it,' without exploring historical byways."

Hughes-Hallett, D., P.F. Lock, A.M. Gleason, D.E. Flath, S.P. Gordon, D.O. Lomen, D. Lovelock, W.G. McCallum, B.G. Osgood, A. Pasquale, J. Tecosky-Feldman, J. Thrash, K.R. Rhea, & T.W. Tucker. 2009. "Applied Calculus." Wiley, fourth edition, publisher's information at <http://bit.ly/Kl2qQz>  Amazon.com information at <http://amzn.to/KiDnvH>, note the searchable "Look Inside" feature. For other books by Hughes-Hallett, et al. see <http://amzn.to/HWUcQV>.

Kline, M. 1998. "Calculus: An Intuitive and Physical Approach."  Dover. Amazon.com information at <http://amzn.to/LsOYKC>, note the searchable "Look Inside" feature. First published in 1967.

Ohanian. H.C. 2009. "Einstein's Mistakes: The Human Failings of Genius." W.W. Norton, publisher's information at <http://bit.ly/13quVq3.>. Amazon.com information at <http://amzn.to/11qwxlb>, note the searchable "Look Inside" feature. See also Weinberg (2005).
Renfro, D.L. 2013a. "Re: Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?" online on the OPEN! Math-Teach archives at <http://bit.ly/V2aR9q>. Post of 15 Jan 10:23 AM (the MathForum fails to specfy the time zone).
Renfro, D.L. 2013b. " Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?" online on the OPEN! Math-Teach archives at <http://bit.ly/W4bLB5>. Post of 14 Jan 4:27 PM (the MathForum fails to specfy the time zone).

Weinberg, S.  2005.  "Einstein's Mistakes: Science sets itself apart from other paths to truth by recognizing that even its greatest practitioners sometimes err," Physics Today, November, pp. 31-35; online as a 336 kB pdf at <http://bit.ly/VSyoLL>>

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Re: Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?

Louis Talman
In reply to this post by Robert Hansen
On Tue, 15 Jan 2013 09:58:46 -0700, Robert Hansen <[hidden email]> wrote:

> Other than your's (and mine) puzzlement over the author's statement  
> regarding "working out the problems", isn't this just the expected and  
> unavoidable consequence of people studying what they weren't meant to  
> study, and then telling us of it?
>


That's a nice, if inadvertent, confession regarding your study of  
education, Bob.

- --Lou Talman
   Department of Mathematical & Computer Sciences
   Metropolian State University of Denver
   <http://rowdy.msudenver.edu/~talmanl
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Re: Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?

Robert Hansen

On Jan 15, 2013, at 3:41 PM, Louis Talman <[hidden email]> wrote:

That's a nice, if inadvertent, confession regarding your study of education, Bob.

What? The only modification I would have made is to add one word, "harmless". Here, try this...

"isn't this just the expected, unavoidable and harmless consequence of people studying what they weren't meant to study, and then telling us of it?"

What is your problem with it now? The word "meant"? I tried other words, like "prepared", "interested", "available", "able". I think "meant" covers all contingencies, including not "meant" to study that particular treatment yet. The point is, the person is telling you at the end, "I don't get it."

Bob Hansen
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Re: Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?

Michael Paul Goldenberg
In reply to this post by Richard Hake
At the risk of interrupting the speculation-fest about Susan Ohanian's thinking and intent, perhaps one of the fun seekers could have the decency to contact her and ask. It's not exactly hard to find her contact information on-line.

Frankly, though, I do wonder about Richard Hake's decision to share an anecdote from a list that is not open to the public,  with folks in this particular venue, given the predictable comments it has evoked. We now have a few of the usual snakes and vipers commenting on Susan Ohanian, a very bright person indeed. I think he has done her a serious disservice, particularly if he didn't request permission beforehand.
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Re: Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?

GS Chandy
In reply to this post by Richard Hake
Robert Hansen (RH) posted Jan 15, 2013 10:28 PM:
> Other than your's (and mine) puzzlement over the
> author's statement regarding "working out the
> problems", isn't this just the expected and
> unavoidable consequence of people studying what they
> weren't meant to study, and then telling us of it?
>
> Bob Hansen
>
What, in your opinion, are the things that people

"weren't meant to study"

versus the things that they

"*were* meant to study" ???

Do I perhaps see shades of a 'new Inquisition', of sorts, that you plan to put upon us?

GSC
("Still Shoveling!")
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Re: Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?

Louis Talman
In reply to this post by Robert Hansen
On Tue, 15 Jan 2013 14:02:39 -0700, Robert Hansen <[hidden email]> wrote:

On Jan 15, 2013, at 3:41 PM, Louis Talman wrote: That's a nice, if inadvertent, confession regarding your study of education, Bob.


What?


The only modification I would have made is to add one word, "harmless". Here, try this... "isn't this just the expected, unavoidable and harmless consequence of people studying what they weren't meant to study, and then telling us of it?" What is your problem with it now? The word "meant"? I tried other words, like "prepared", "interested", "available", "able". I think "meant" covers all contingencies, including not "meant" to study that particular treatment yet. The point is, the person is telling you at the end, "I don't get it."


I don't know whether the amended statement applies to your study of education or not. My suspicion is that it's nearly correct once you add the word "harmless".  After all, as has been pointed out, your "study" affects primarily (only?) a few people---whose minds you will not change.

--Lou Talman
  Department of Mathematical & Computer Sciences
  Metropolitan State University of Denver
<http://rowdy.msudenver.edu/~talmanl>
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Re: Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?

GS Chandy
In reply to this post by Richard Hake
Responding further to Dave Renfro's of Jan 15, 2013 2:57 AM:
Whenever I am tempted to lie or exaggerate or boast
about something, Mark Twain's famous saw comes to mind:

"The best reason for telling the truth is that you never
have to remember ANYTHING!" (words/ideas to that effect).

It came again to mind when I read through the boast of that 'literature lady' (if I may thus refer to her) about whom Richard Hake told us.  As she (or someone) seems to have recounted the tale:
+++

>
> * I like to tell the story that Hans, a newly minted
> Ph.D. in physics was
> * stunned to find out he was married to somebody who
> never took calculus.
> * I don't know quite what he expected from an MA in
> medieval literature,
> * but the first year we were married he gave me an
> ugly calculus book for
> * Xmas, explaining it was a classic in the field
> (Courant). The second
> * year we were married I gave him a notebook with the
> problems worked out.
> * I never seemed to gain any insight from this
> exercise, which struck me
> * then as plodding and now I don't have any idea what
> any of it means.
> * Nonetheless, doing calculus for love is a far
> better reason than the
> * one promoted by Obama, Duncan, Bill Gates, et al.
+++
On considering that story in a little more depth, it seems to be almost ENTIRELY falsehood (or, at least,
EXTREMELY strange):

Hans did not know when he married the literature lady that his future wife had NEVER done anything in calculus?  

That, to me, appears passing strange - but put it down to the VERY 'fast' life you guys lead in the US these days.

This literature lady claims her husband (Hans), wanting to acquaint her with a classic of mathematics, gave her "an ugly calculus book" (the Courant book) the first year they were married - and the second year she just gave him a notebook "with the problems worked out".  

Just consider some of the implications of that statement.

- -- Not "some of the problems" worked out.

- -- Not "problems worked out".  

- -- NO!! - she just gave him a notebook with "the problems worked out".  Implying a) that she had worked out "ALL the problems" (as Dave Renfro has pointed out); and moreover b) that she had found it all to be simply an utter breeze!!

I now seem to recall that some of the problems in the Courant were not just 'challenging', but a few were indeed extremely difficult.  And I was REALLY rather good at Calculus those days!  I believe there were a few of those problems that I wasn't on my own able to work out.  I was able to work  them out only after a good bit of discussions with classmates and teachers.

This wonderful literature lady - she just handed her husband "a notebook with the problems worked out"!  A veritable breeze indeed!!!

Amazing!  The literature lady was a complete novice when she was given the Courant book.  

She didn't even bother to discuss any of the problems or math processes involved with her Ph.D. (Physics) husband: a year later, she just nonchalantly handed him that famous notebook with "the problems worked out"!

I think many of us might have read Aldous Huxley's famous and touching story "Young Archimedes", where (if I recall rightly) the storyteller meets a young Italian boy, say about 10-12 years in age, whose gifts in mathematics are so stupendous that he, the storyteller, feels like getting down on all fours and wagging his tail!  (Something to that effect).

The literature lady's feat (breezing through all the Courant problems) was, I agree, not a patch on what "Young Archimedes" did (he INVENTED, for himself, the entire Pythagoras Theorem!) - but surely she must have been some small part of the way there?

I do believe the literature lady's husband, Hans, should urgently get himself down on all fours before her and wag his tail.

And, if Hans would PLEASE introduce me to his genius wife, I shall IMMEDIATELY get myself down on all fours and wag *my* tail!

Further: how come the literature lady did not, after that remarkable feat of mathematical intuition and understanding,  do anything more in math later?   Did her husband perhaps prevent her, out of 'male jealousy' or some such reprehensible trait to which we males are often subject?

How come that notebook is not treasured in some museum of mathematics?

These are 'mysteries' to be solved.  

Or lies to be uncovered: and the literature lady's husband, Hans, might like to remind her of Mark Twain's aphorism.

GSC
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Re: Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?

GS Chandy
In reply to this post by Richard Hake
Michael Paul Goldenberg (MPG) Jan 16, 2013 8:24 AM :

>
> At the risk of interrupting the speculation-fest
> about Susan Ohanian's thinking and intent, perhaps
> one of the fun seekers could have the decency to
> contact her and ask. It's not exactly hard to find
> her contact information on-line.
>
> Frankly, though, I do wonder about Richard Hake's
> decision to share an anecdote from a list that is not
> open to the public,  with folks in this particular
> venue, given the predictable comments it has evoked.
> We now have a few of the usual snakes and vipers
> commenting on Susan Ohanian, a very bright person
> indeed. I think he has done her a serious disservice,
> particularly if he didn't request permission
> beforehand.
>
To me it appears that, from what Susan Ohanian claims to have accomplished (simply BREEZING through all the problems of the Courant calculus book despite NEVER  having taken calculus!), she is MUCH more than merely "very bright".

I am one snake/viper who has commented.  The message does not appear to have appeared yet, so I have re-sent it, with some modifications to the earlier one - before I saw this message of MPG's.  (My modifications did not make the message any less 'snakish'/ 'viperish').  I would have sent it anyway.  If it doesn't appear, I shall inquire with the Moderator as to why not.

I stand by that post (assuming it is published).  I do not see ANY reason why I should, as MPG has suggested, "have the decency to contact Ms Susan Ohanian and ask". She, not I, made certain claims which, to me, appear untenable.  Those claims were published.  

How does it become my duty to ask her anything?

If she had shown a little respect and had not referred to the Courant classic as an "ugly calculus book" (words to that effect), I may not have responded quite so 'snakishly'/ 'viperishly'.

As to why Richard Hake might have published that little beaut of story, he should clarify that himself.  Idle speculation: Perhaps he too was as offended as I have been.

GSC
(Snake/Viper-in-Chief)
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Re: Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?

Robert Hansen
In reply to this post by GS Chandy

On Jan 15, 2013, at 10:06 PM, GS Chandy <[hidden email]> wrote:

What, in your opinion, are the things that people 

"weren't meant to study" 

versus the things that they 

"*were* meant to study" ???

You don't know until you try.

Bob Hansen
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Re: Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?

Robert Hansen
In reply to this post by Michael Paul Goldenberg

On Jan 15, 2013, at 9:54 PM, Michael Paul Goldenberg <[hidden email]> wrote:

> At the risk of interrupting the speculation-fest about Susan Ohanian's thinking and intent, perhaps one of the fun seekers could have the decency to contact her and ask. It's not exactly hard to find her contact information on-line.
>
> Frankly, though, I do wonder about Richard Hake's decision to share an anecdote from a list that is not open to the public,  with folks in this particular venue, given the predictable comments it has evoked. We now have a few of the usual snakes and vipers commenting on Susan Ohanian, a very bright person indeed. I think he has done her a serious disservice, particularly if he didn't request permission beforehand.

He also shared the comments from here as well, but not in whole of course, only snippets taken out of context, along with the author's name. Pleading with him to stop isn't going to help. I have seen others try. That just increases the likelihood that your plea gets its own tiny url and placed out of context in his next iteration of spam.

Bob Hansen
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Re: Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?

GS Chandy
In reply to this post by Richard Hake
Robert Hansen ('Bob') posted Jan 16, 2013 2:05 PM:

>
> On Jan 15, 2013, at 10:06 PM, GS Chandy
> <[hidden email]> wrote:
>
> > What, in your opinion, are the things that people
> >
> > "weren't meant to study"
> >
> > versus the things that they
> >
> > "*were* meant to study" ???
>
> You don't know until you try.
>
> Bob Hansen
>
Thank you, Bob.  I'm somewhat mystified (as no doubt the victims of the Inquisition were, too) - but thank you anyway.

GSC
("Still Shoveling!")
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Re: Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?

Michael Paul Goldenberg
In reply to this post by Richard Hake
Perhaps, but I have an advantage you do not: I'm a member of the list and a friend of Ms. Ohanian. Hence, I posted a similar message on the list. I have long blocked Professor Hake's messages, and so I'm only seeing these because I'm reading this list on the web archives. Much as it pains me to deal with him, I only mentioned it here as an appeal to the decency of those who are currently running wild with speculations about Susan and her husband, Hans, hoping that they will contact her and/or him, rather than continue to engage in pointless interpretations based on Hake's version of things. On the original list, I think things may go a bit differently.
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Re: Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?

Michael Paul Goldenberg
In reply to this post by Richard Hake
GS, please stop. Contact Susan Ohanian directly (she has a web site) and stop these foolish speculations and exaggerations. It's insulting to two people you would do well not to mock, particularly not based on Richard Hake's post.

Thanks in advance.
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